Answer:
The difference in monthly payments between the two offers is $32.2
Step-by-step explanation:
He already has $11,000 saved, thus, the amount remaining to pay is $62,000-$11,000 = $51,000
Now, incentive A is taking off 7,000 off the price of the car but the framing amount is a loan at 5.85%
Thus the amount of loan to be taken will be 5.85% on (51,000-7000) = 44,000
So the amount to be paid monthly via incentive A is calculated using the formula below
Monthly payment = P(r/n)/[1-(1+r/n)^-nt]
Where P = 44,000
r is the rate = 5.85% = 5.85/100 = 0.0585
n is the number of months per year = 12
t is the time in years = 4 years
Substituting the values, we have;
Monthly payment = 44,000(0.0585/12)/[1-(1+ 0.0585/12)^-60] = 44,000(0.004875)/[1-(1+0.004875)^-48] = 214.5/(0.2081) = $1030.3
Incentive B however, involves paying the 51,000 over 4 years.
The monthly payment here will be 51,000/48 = $1,062.5
Thus, the difference between the two payments will be;
$1062.5 - $1030.3= $32.2
